Secular Evolution of Pre-Main Sequence

Triples

Erez Michaely

Advisor : Prof. Hagai Perets

Israel Institute of Technology, Haifa

Observations : Binaries

Introduction

• Close Low Mass binaries are likely to be a part of a triple system [Tokovinin 2006]

• O stars: Period distribution favors shorter periods than Opik law (log uniform) [Sana 2012]

Triples are very common

Introduction

•~15% of all stars reside in triple [Raghavan 2010]

•Possibly >50% of stars with M>5Msun are in triples [Remage Evans 2011 ]

•Vast majority of multiple systems are hierarchical [Tokovinin 1997]

Hierarchical Triples

Introduction

Previous Work : Eggleton & Kiseleva

Introduction

Kozai Cycles Tidal Friction• Harrington 1968• Mazeh & Shaham 1979• Kiseleva et al. 1998 used KCTF on the Algol system • Eggleton & Kiseleva 2001 and 2006 : KCTF might produce many close/contact binaries• Facrycky & Treaine 2007• Perets & Naoz 2013 – planetesimals• Many more. . .

•The calculation were made on MS systems

Previous Work : GR dissipation

Introduction

• Work have been done also for compact objects• Instead of tidal dissipation GR radiation• [Blaes et al. 2002]

Pre Main Sequence properties

Introduction

Pre-MS•Very big; size of giants•Convective•Contracts on a thermal timescale

•Good objects to undergo tidal friction

Pre Main Sequence properties

Introduction

Secular Evolution scheme of Pre-MS triples

Introduction

3

21

Pre-MS circular binary

Secular Evolution scheme of Pre-MS triples

Introduction

3

21

Pre-MS contraction & Kozai oscillation

Secular Evolution scheme of Pre-MS triples

Introduction

3

21

Eccentric orbit induces tidal interactionDissipation of orbital energy

Tidal Friction•Simple model for equilibrium tides

Hut 1981 Model for equilibrium tides

8da R

dt a

Introduction

Stellar evolution parameters taken from MESA

Introduction

• MESA (Paxton 2010) stellar evolution code• Radius as a function of time• Radius of gyration

Secular dynamics up to an octupole expansion

Introduction

• Double averaged Hamiltonian, secular code [Michaely & Perets

2014] following [Ford 2000,Blaes2002]• Actually very similar to the code described by Silvia

• Two interacting rings • Equation of motion for the orbital elements

• Relevant timescales

3 12 2

312 2

3 22 2 0 1

2

2 1

2 1a e m mt

G m a

5 1 32 2 2

512 2

4 2 22 2 1 0 1

3

2 0 1 2 1

2 1 1a e e m mt

G m m m e a

ExampleKCTF on the Pre-MS for Low Mass Stars

Preliminary results

0 1 sunm M

1 0.5 sunm M

2 1 sunm M

1 2[AU]a

2 50[AU]a

1 0.01e

2 0.2e

70i

KCTF on the Pre-MS for Low Mass Stars

Preliminary results

No Tides

KCTF on the Pre-MS for Low Mass Stars

Preliminary results

With Tides

ExampleKCTF on the Pre-MS for High Mass Stars

Preliminary results

0 15 sunm M

1 20 sunm M

2 10 sunm M

1 8[AU]a

2 100[AU]a

1 0.01e

2 0.2e

70i

KCTF on the Pre-MS for High Mass Stars

Preliminary results

No Tides

KCTF on the Pre-MS for High Mass Stars

Preliminary results

With Tides

ExampleKCTF on the Pre-MS for High Mass Stars induce RLOF

Preliminary results

0 15 sunm M

1 20 sunm M

2 25 sunm M

1 8[AU]a

2 80[AU]a

1 0.01e

2 0.8e

80i

Preliminary results

With TidesKCTF on the Pre-MS for High Mass Stars induce RLOF

Coupling orbital energy with tidal interaction - helps

Energy Budget• Orbital energy is dissipated into the inner binary• The energy deposited into the star in for of heat• Heat inside the proto-star ‘help’ fight against the gravitational collapse• The pre-MS is longer, hence the mechanism is more efficient• Future work

Kozai-Lidov Oscillations

Summary•Triple dynamics and evolution is a reach field the implications on a variety of astrophysics aspects•Secular code with mass loss / transfer and tidal friction and stellar evolution was developed•Secular evolution in the Pre-MS phase is important• Period distributions• Mass function

•Systematic exploration of parameter space is available•A lot more can be done•Comments are welcomed•Stay tuned. . .

Summary

Thank you